Create a new column named "Begin Date", make it calculated, add "=[Start Time]" in formula, return type of date and time, uncheck add to default view.Create a new view "Future events" (or similar) based on standard format, on filter - select "Show Items only when the following is true", select "Begin Date", select "is greater than or equal to", enter "[Today]" in field, click OK to save new view.

Keep in mind that this will also filter out events that have started but have not yet ended. An alternate approach would be to set your custom field to equal the End Time field.

Another SharePoint customization blog offers a way to use a custom yes/no field that calculates if the event has passed.